Problem: Simplify the following expression: $q = \dfrac{15p + 45}{-5}$ You can assume $p \neq 0$.
Find the greatest common factor of the numerator and denominator. The numerator can be factored: $15p + 45 = (3\cdot5 \cdot p) + (3\cdot3\cdot5)$ The denominator can be factored: $-5 = - (5)$ The greatest common factor of all the terms is $5$ Factoring out $5$ gives us: $q = \dfrac{(5)(3p + 9)}{(5)(-1)}$ Dividing both the numerator and denominator by $5$ gives: $q = \dfrac{3p + 9}{-1}$